The 25-year-old joined the Foxes in a £13m move from Nice last summer. However, his first season in England was blighted by injuries, and he could manage only four league appearances for the Foxes last season.
"I heard about the interest of Nantes but neither me nor my adviser have been contacted," Mendy said, according to L'Equipe.
"Anyway, since my adviser talked to me about the possibility of joining Bordeaux, I'm set on it.
"I've lost a year in England because of a failed ankle surgery, which unfortunately necessitated a second operation in March. Even though I am not 100 per cent yet, I have just returned from an excellent rehabilitation phase.
"And now I have the hope of rallying the Girondins (Bordeaux) fairly quickly. It's even an obsession."
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